Leaders of a union representing thousands of transit workers have pledged support for an independent audit of the pension system of the Massachusetts Bay Transportation Authority.

The statement released Thursday by Carmen's Union president James O'Brien and James Evers, the union's secretary/treasurer, follows a report that raised questions about the strength of the $1.6 billion fund.

The report by Harry Markopolos, a whistleblower in the Bernard Madoff fraud case, and Boston University professor Mark Williams said the fund may have overstated its financial position by $470 million.

That prompted former state Treasurer Steven Grossman, an MBTA Retirement Board member, to call for an independent review of the fund.

O'Brien and Evers, who also sit on the board, said they backed an "immediate, open and complete audit" of the pension system.